Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C17×#123 ⋊ C2 |
| Sylow | C17 ⋊ #2681 |
618 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1088 |
Polycyclic presentation:
2^7,17|a^2=f,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^16,c^b=cg,d^b=de256 conjugacy classes — view the full character table.
| maximal subgroup of | #17241268, #17241275, #17241294, … |
| maximal normal subgroup of | #17241268, #17241275, #17241294, … |
| maximal quotient of | #16961645, #16961654, #16961678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 10862);